Use the etchings to position the ring dead center. Using the larger adhesive rings as a jig may work for you. The adhesive tends to stick with even gentle pressure, so alignment is tricky. If you mess up, you can remove the adhesive and use Ambroid or model aircraft cement.

Here's the final assembly, using 1" #4 screws to hold the stack together. Make sure that the LED pokes through the hole in the plastic. You may also replace the LED with other colors. The blue plastic is UV-reactive, but goes for blue or white light as well.